What’s a ‘bit’?

What’s a ‘bit’?

Bit is such a little word. A bit short. A bit overlooked.

But it’s easy to bite off a bit too much. That’s why I won’t be exploring all possible meanings of bit—because there are many. From ‘a small or unimportant part’ through to things you use to drill holes or stick in a horse’s mouth.

The bit that’s been buzzing around my head lately is a newer definition: Bit—meaning ‘binary digit’, first used in 1948. As in a 1 or a 0—an on or an off. It’s the smallest meaningful ‘bit’ of information we tend to talk about.

This is the bit we hear when people speak of 64-bit processors or 256-bit encryption. It is the same bit that when combined with 7 others makes up a byte. We take 1024 bytes and we have a megabyte. Take a 1024 megabytes and we have a gigabyte. Take 1024 of those and we have a terabyte.

You’ll notice all these numbers are divisible by 2. That’s the ‘bi’ part of bit, as in ‘binary’. It’s also ties in to the simplest example of exponential growth.

Things start slow, then start to get big very quickly. But that last number above (32896) is only 2 to the power of 15. When we talk about 256-bit encryption, we’re talking about 2 to the power of 256 possibilities. This is a spectacularly large number.

Two to the power of 20 is over a million (1,048,576), 2 to the power of 21 is double that… But we have much further to go.

Two to the power of 30 is well over a billion (1,073,741,824). Two to the power of 40 is over a trillion. Two to the power of 50 is 1 quadrillion, give or take 125 trillion or so.

Now we start to enter space maths. While you will have heard of trillions, used to describe things like the world economy, or the number of ants on Earth (10–100 Trillion), a quadrillion (that’s a 1 with 12 zeros behind it) starts to get more esoteric. One quadrillion seconds is called a ‘petasecond’, and is approximately 32 million years.

But we’re still not remotely close to the number of possibilities with 256 bits.

At 2 to the power of 60, we’re over 1 quintillion; at 2 to the power of 70, it’s over 1 sextillion. Two to the power of 80 is over 1 septillion, also known as a trillion trillion, which is about 100 times the number of stars in the observable universe. (Despite hearing this term many times, I only recently learned what it means: If the universe is only 13.8 billion years old, and nothing can travel faster than light, then we can’t see any further than how far light could travel in 13.8 billion years—this is the ‘observable universe’. It’s about 93 billion light years across and contains more stars than the Earth has grains of sand.)

Two to the power of 90 is over an octillion. Two to the power of 100 is more than a nonillion.

Despite the absurd enormousness of this number, compared to 2 to the power of 256, you wouldn’t see it on any graph. A nonillion is less than 0.0000000000000000000000000000000000000000000001% of 2 to the power of 256. Two to the power of 256 is:

Which is so stupidly big that I can’t even find a way of visualising it. I attempted to rationalise it as a number of seconds… and got this: ≈ 2.7×10^59 × universe age. That’s 27 with 58 zeros behind it times the age of the universe.

Times the age of the universe in seconds.

This is what 256-bit encryption means. Whereas you have a 1 in 10,000 chance of guessing a 4-digit PIN, your chance of guessing a 256-bit encryption key is 1 in 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936.

Because, if you’re viewing this on a mobile phone, that number will be cut off due to the commas, here it is with spaces as the separator, so it doesn’t wrap: